The design of electronic data transmission systems requires adequate filters for frequency selective filtering. Such filters preferably implemented as integrated circuit devices must not only be compatible with other system components but they should utilize a minimum of silicon chip area, have a high dynamic range, provide gain in the passband and should have zeros of transmission at zero frequency in order to realize high pass filtering.
Prior to the present invention, filters were suggested using switched capacitors and operational amplifiers. The basic building block of such circuits was usually a sampled-data integrator, obtained by replacing the resistor in an R-C active integrator with a switched-capacitor resistor. This approach, however, presented certain problems because the mere replacement by switched capacitors does not simulate the equivalent resistors exactly. Distortion in the frequency response of such circuits occurred because of the imperfect mapping of the frequency variables when transformed from the s to the z plane. Circuits utilizing a grounded capacitor in conjunction with two switches to replace a resistor are discussed in IEEE Journal of Solid State Circuits, Vol. SC-12, No. 6, pp. 392-599 and pp. 600-608, Sec. 1977. For such circuits, the mapping between the frequency variables is given by the formula s.fwdarw.(z-1)/T, which is equivalent to replacing derivatives in the differential equation of a continuous system with forward differences. In order to keep a close match between the performances of the continuous and discrete-time systems, the clock rate 1/T must be chosen much higher than the highest frequency present in the signal. In another prior technique, the switched capacitor that replaced the resistor had a special configuration based on the trapezoidal integration. Thus, it performed a conformal mapping from the s plane to the z plane and eliminated the disadvantages mentioned above. The resulting discrete-time response is related to that of the continuous-time model through the bilinear transformation defined by: ##EQU1## A significant disadvantage of this latter approach is that the difference of two signals or the negative of a signal cannot be obtained as easily as with the grounded switched-capacitor "resistor." In order to exploit this ease of design inherent in the grounded switched-capacitor circuit, and at the same time compensate for the s-to-z plane mapping defects, a direct z-domain synthesis should be carried out. The present invention describes a filter section that provides a solution to this problem.
Another problem which has been overcome by the present invention is that of providing a third order filter section that eliminates analog components in an output sample-and-hold sub-section.